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Trigonometry emerged in the Hellenistic world during the 3rd century BC through the application of geometry to astronomy.
Trigonometry developed from ancient efforts to study angles, lengths, and astronomical positions. Sumerian and Babylonian scholars explored angle measurement and ratios in similar triangles, while Greek mathematicians such as Euclid and Archimedes investigated chords and inscribed angles geometrically. In the 2nd century BC, Hipparchus compiled the first known trigonometric table of chords, and Ptolemy later produced detailed chord tables in the Almagest, which remained influential for more than a millennium. Indian mathematicians introduced the sine function and developed early tables of trigonometric ratios. During the medieval period, Islamic mathematicians translated and expanded Greek and Indian work, developing tables for cotangents and all six trigonometric functions. Nasir al-Din al-Tusi established trigonometry as an independent mathematical discipline and significantly advanced spherical trigonometry. Knowledge later reached Western Europe through Latin translations, where scholars such as Regiomontanus, Copernicus, Pitiscus, Viète, Euler, Gregory, Maclaurin, and Taylor helped shape modern trigonometry. Its applications expanded from astronomy to navigation, surveying, geodesy, engineering, physics, and signal analysis.
Trigonometry emerged in the Hellenistic world during the 3rd century BC through the application of geometry to astronomy.
Hipparchus compiled the first known trigonometric table using chord lengths, while Ptolemy created more detailed tables in the Almagest.
Indian mathematicians introduced the sine function and produced some of the earliest tables of trigonometric ratios.
Medieval Islamic scholars translated, preserved, and expanded Greek and Indian trigonometric knowledge, including the development of cotangent tables and all six trigonometric functions.
Nasir al-Din al-Tusi is widely credited with establishing trigonometry as an independent mathematical discipline and advancing spherical trigonometry.
During the Renaissance and early modern period, trigonometry spread through Europe and developed into a major branch of mathematics driven by navigation, surveying, astronomy, and mapmaking.
Later developments included trigonometric series, complex-number representations, and applications in physics, engineering, acoustics, optics, and communications.
A line segment joining two points on a circle, used by ancient Greek mathematicians as an early basis for trigonometric calculations.
A Greek astronomer and mathematician traditionally regarded as the father of trigonometry because he compiled the first known table of chords.
A major Greek astronomical treatise containing detailed tables of chord lengths that supported trigonometric calculations for centuries.
A trigonometric function first systematically developed in India, relating an angle to a ratio associated with a right or spherical triangle.
A Persian mathematician who produced accurate sine and tangent tables and used all six trigonometric functions by the 10th century.
A Persian polymath who developed trigonometry as an independent mathematical discipline and advanced the study of spherical triangles.
The study of relationships among angles and sides of triangles drawn on the surface of a sphere, especially important in astronomy and navigation.
A surveying and navigation method that determines distances or positions by measuring angles in a network of triangles.
Infinite sums of sine and cosine functions used to represent periodic and other functions in mathematical analysis.
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